# Demonstrations on Force on a Conductor in Magnetic Field

Following demonstrations on force on a conductor in magnetic field can be performed at home or in the classroom.

## Force on a straight wire

The force on a current carrying wire placed in a magnetic field is given by $\vec{F}=I\vec{l}\times\vec{B}$.

Take about 1 cm wide and 10 cm long aluminium foil. The kitchen foil works very well. On a flat wooden surface, tape about 2 cm of the strip from each end. The middle portion should be very loose. Press this portion to touch the surface at the middle. Place two ring magnets in vertical position on the sides of the strip so that their magnetic filed at the strip adds up. Thus, the magnetic field is perpendicular to the length of the strip and horizontal. Now connect the two ends of the strip to battery through a switch.

Press the switch and see what happens to the strip. Did the middle portion jump? If not, reverse the direction of current. Now, it will jump up.

The current and magnetic field are both in horizontal plane. Hence, the force on the middle portion is vertical. For one direction of the current, force will be upward and for another direction, it will be downward. You can also change the direction of magnetic force by changing direction of the magnetic field.

## Magnetic Swing

Oersted discovered that a current carrying conductor experiences a force when placed in a magnetic field.

In this demonstration we make a magnetic swing which moves by this force. We can learn more about the direction of this force and the factors which affects its magnitude.

### Apparatus

Two metal bars (or two cycle spokes), a wooden base (or a cardboard base), copper wires, battery, two ring magnets, crocodile clips.

### Procedure

1. Fix the metal bars in the wooden base at some distance from one another.
2. Make small loops with some copper wire at the upper end of the two bars.
3. Take a single copper wire, give it the shape of swing and hang it from the two metal bars from the loops made above. Make sure that the copper wire swings freely from the loops.
4. Connect the two metal bars to a battery with the help of crocodile clips and copper wires. The circuit is now complete.
5. Place a ring magnet below the swing.
6. Switch on the power source. See the deflection of the swing.
7. Flip over the ring magnet. See that the deflection is now in the opposite direction.
8. Interchange the terminals of the battery. The deflection again gets reversed.
9. Take out the crocodile clip from one of the metal bars to disconnect the circuit. Now touch it again with the metal bar. See the copper wire swing to and fro.
10. Increase the voltage in the battery. Repeat the above process and see that wire swings with a greater amplitude.
11. Now put two ring magnets instead of one below the swing. Again repeat the process and see the increase in amplitude of the swing.

### Discussion

When the power is switched on, a current $$i$$ passes through the copper wire. In the magnetic field $$\vec{B}$$ of the ring magnet, current carrying wire experiences a force $$\vec{F}$$ given by

$$\vec{F}=i(\vec{l}\times \vec{B}),$$

where $$l$$ is the length of the conductor. The direction of this force is given by the right hand thumb rule. When the direction of magnetic field reverses on flipping over the magnet, the direction of the force also reverses. Similarly when the current direction is reversed, the force also reverses direction.

Increasing the voltage of the battery increased the current which in turn increased the magnitude of the force and the amplitude. When instead of one magnet we put two magnets the magnetic field strength increases causing the force to increase again.

An interesting observation: If the magnet is given a to and fro motion near the current carrying copper wire it starts swinging. This can be explained on the basis of Lorentz force experienced by the wire.

Now the magnet is removed and only the fingers make the to and fro motion. The wire again starts swinging!

In another variation the current source is removed from the copper wire and the magnet is given a to and fro motion in the vicinity of the copper wire. Interestingly the copper wire again starts swinging!

Is it phenomenon of resonance which we are seeing or something else?

Puzzle: This set-up can be used as an interesting puzzle. Ask the students to find poles (north/south) of ring magnet by using this set-up. This will eliminate the confusion about Fleming's right hand rule/ left hand rule/ screw rule etc.

## Force between parallel wires

When two parallel wires are placed close to each other then they attract each other if direction of current is parallel and repel each other if direction of current is anti-parallel. This can be explained by seeing the force on a current carrying wire placed in the magnetic field of the other wire.

Make two coils (radius 2 cm, number of turns 100). Hang these coils with their planes parallel to each other. Connect both coils to a battery/power supply. See attraction/repulsion between them by changing direction of current.

This demonstration is to show attraction and repulsion between current carrying conductors. A current carrying coil acts as a magnet. The direction of magnetic field (or the location of north and south poles) depends on the direction of current flowing through the coil. When current direction is same in both the coils then direction of magnetic field is same and they acts as if north pole of one coil is placed close to south pole of another coil. So they attract each other. When current direction is opposite in two coils then their magnetic fields are opposite and they acts as like poles of two coil are close to each other. Thus, they repel each other.

## Electromagnetic train

This experiment is a direct demonstration of the force law $\vec{F}=I\vec{l}\times\vec{B}$.

You need a DC power supply, two parallel copper wires pasted on a fiber base with marks A and B. Aluminium foil, pen body/refill, speaker magnet.

### procedure

1. Put the speaker magnet on the working table with a flat surface resting on the table. Place the fiber base on the magnet so that the two wires are symmetrically placed on the magnet. Connect with the DC power supply. Do not switch on.
2. Wrap the aluminium foil on the pen body/refill in such a way that the total length is almost same as that of the body. Start with placing the a triangular corner of the given foil on the pen body and start wrapping. As you wrap, it will go on up the body and at no place the thickness will be more 2-3 layers.
3. Press the final loose end of this roll. This will fix it firmly.
4. Gently pull the pen body out of the rod. Take care that the roll itself retain the cylindrical structure.
5. Place the roll on the two copper wires, perpendicular to them and symmetrically about the center of the speaker magnet.
6. Now switch on the power supply. Look at the roll. Which direction did the roll go? Towards the mark A or B on the base?
7. Place the roll at different positions on the track (wires) and repeat. Write your observations.
8. Invert the magnet and repeat step-6. Which direction did the roll go? Towards the mark A or B on the base?
9. From these observations identify which side of the speaker magnet is north.

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